CERTAIN HARMONIES OF THE SOLAR SYSTEM. 73 



(103) The analogies to the great planetary system, presented by the satellite 

 systems, have been discussed, in another connexion and aspect, in (58) and (59). 



Possible Succession of Changes, in the Progress of the Division, Recombination, and 

 Final Separation of the Great Masses of the Solar System. 



(104) In the Ancient State contemplated in (44) and in Table (F) in (45), the 

 relation of masses and distances was, it would seem, very nearly the same with that 

 of the existing masses and distances of Jupiter and of Saturn as exhibited in (53); 

 viz., that in which m(r)^ of the one = m'(r')^ of the other. 



For — retaining the symbols in (44)— [the second mass in order in Table (F) 

 in (45), including in itself the masses of Uranus and Saturn, Avhile the first mass 

 is that of Neptune]; we have in the instance of the second mass 



mXr'f of [(U)>^] = 0.05090861; 

 and for the first, 



mr"■■^! = 0.0458582 ; 

 the ratio of the two being 



«^WofI(U)^]_iiioi. 



which, since mr'^, thus, nearly = m\r'y, gives 



m . (r'y _ 

 tn' r^ 



or the masses nearly in the inverse ratio of the squares of the distances. 



Next, comparing the mass and distance of Neptune — also those of the whole- 

 planet (U), made up of Uranus and its (now) missing interior half-planet §i — and 

 then, the mass and distance of i^, that is of Saturn in its ancietit state before, (43), 

 S» was absorbed [the mass of $,i being deduced as in (41)] ; we shall obtain for 

 the several ratios of the distances and the inverse ratio of the f powers of the 

 masses, respectively : 



distof^W _ i.j^^o (m;)lof^) ^ j_^gg^_ 



dist. of (U) ml of tjj 



dist. of (U) ^ ijQQg. (m")l of >^ ^ 1.7125.1 



dist. of >^ ' ' {m'Ji of (U) 



And then, with respect to the existing Saturn and Jupiter, we have, as in (53), 



TO"'(r"')- of b = 0.0259S5 ) 

 m"Xr")' of Ji = 0.025832 | ' 



a coincidence more perfect than that found in the instance of the two outer great 

 masses, in which the data to be used are less accurately ascertained. Then here, 



' It is at least curious that Saturn deprived of the mass of St (z. e. the ancient Saturn) must here 

 once more enter into the computation instead of the existing planet. 



10 February, 1875. 



